Re: qestion on radian

ok so a radian is the raduis and the radius is half a diameter of a circle.

this the video ive watched

my question is how do i measure the circumfrence of a circle. I have seen the measurement of the circumfrence of a circle approximatley is 3.14 .(this know as pi
A ruler cant measure the distance as ruler is designed as a straight line. I know later there will be no need for me to measure the perimetre of a circle. I would like to know how its completed. As then i will be able to see how and have better understanding when im writing down the number 3.14

Re: qestion on radian

Originally Posted by hansolo

ok so a radian is the raduis and the radius is half a diameter of a circle.

No, the radius is either a straight line segment from the center to the edge of the circle or the length of that segment. In contrast, as I said in post #2, the radian does not measure lengths, but angles.

Originally Posted by hansolo

my question is how do i measure the circumfrence of a circle. I have seen the measurement of the circumfrence of a circle approximatley is 3.14 .(this know as pi
A ruler cant measure the distance as ruler is designed as a straight line. I know later there will be no need for me to measure the perimetre of a circle. I would like to know how its completed. As then i will be able to see how and have better understanding when im writing down the number 3.14

You are right that later you won't need to physically measure the circumference. Do you know the joke asking how many software engineers are needed to change a light bulb? None; it's a hardware problem. Similarly, mathematicians give the definition and prove properties of the circumference, but they don't generally measure it with a ruler or any other tool.

If you have a physical cylinder whose circumference you need to measure, you can wrap a thread around it, then straighten it and measure its length with a ruler. In fact, wrapping a thread several times and then dividing the result by the number of times will decrease the error of measurement. You can also roll the cylinder or disk on a flat surface and measure the distance between points on the surface that touch the same point on the cylinder. If you have a circle drawn on paper, you can construct a cyclic convex regular polygon (i.e., a polygon with equal angles and sides whose vertices lie on the circle), measure its side with a ruler and multiply it by the number of sides. The more sides, the closer the perimeter is to the circumference (though the measuring error increases as well). In fact, the circumference can be defined as the limit of perimeters of such inscribed polygons as the number of sides goes to infinity.

The above are methods of measuring or defining circumference. An important property of circumference is that its ratio to diameter is (not 3.14 since is an infinite non-repeating decimal fraction and 3.14 is only its approximation). So, if you know the diameter d (which you can measure with a ruler), then you can find the circumference as , and if the radius is r, then the circumference is .